Not expecting a solution worked out for me... I'm stuck and need a
hint. My prof is on vacation this week and is unreachable and the
homework is due the day he returns...

given:

Servo-tracking control problem.

roots of error dynamics equation are:

-4, -2+2j, -2-2j

our physical model is for that of rocket control:

y" - k1 y = k2 B + k3 w,

where w = wind disturbance--an unknown and unmeasurable constant the only measurable physical things are y, ycmd and y'. k1 and k2 >0 and known (but not given--ie we are free to choose a value I assume)

We are to design B so that y approaches ycmd for all t.

ycmd is of the form

ycmd = c1 + c2t

now I know the error equation should look like:

e''' + a3 e" + a2 e' + a1 e = 0;

So....

I plug the roots given into matlab poly() and get a characteristic equation:

e''' + 8e'' + 24e' + 32e = 0;

which meets the hurwitz constraints:

all coeffs >0 and a3

So now my confusion is:

How do I draw a math flow diagram for the physical model, when all I have is an equation in terms of 3rd order error, e?

He wants us to sim this in simulink and then vary/tweak the given roots to see how the servo-tracking changes.

In class he developed B as a PID algorithm, which I understand accounts for the unknown constant wind.

Can anyone give me some direction?

Thanks,

Bo

given:

Servo-tracking control problem.

roots of error dynamics equation are:

-4, -2+2j, -2-2j

our physical model is for that of rocket control:

y" - k1 y = k2 B + k3 w,

where w = wind disturbance--an unknown and unmeasurable constant the only measurable physical things are y, ycmd and y'. k1 and k2 >0 and known (but not given--ie we are free to choose a value I assume)

We are to design B so that y approaches ycmd for all t.

ycmd is of the form

ycmd = c1 + c2t

now I know the error equation should look like:

e''' + a3 e" + a2 e' + a1 e = 0;

So....

I plug the roots given into matlab poly() and get a characteristic equation:

e''' + 8e'' + 24e' + 32e = 0;

which meets the hurwitz constraints:

all coeffs >0 and a3

*** a2 > a1, 8***24 >32 check.So now my confusion is:

How do I draw a math flow diagram for the physical model, when all I have is an equation in terms of 3rd order error, e?

He wants us to sim this in simulink and then vary/tweak the given roots to see how the servo-tracking changes.

In class he developed B as a PID algorithm, which I understand accounts for the unknown constant wind.

Can anyone give me some direction?

Thanks,

Bo